The Rangers sure have a lot of improving to do — and quickly — following Thursday night’s opening 4-1 defeat to the Coyotes in which sloppiness prevailed at both ends of the ice.

“We just made too many mistakes regarding the way we have to play no matter who’s the coach that has nothing to do with it” Brad Richards told The Post following Alain Vigneault’s debut behind the bench. “We want to play a certain way and we’re going to have to work on it if we want to get there.

“We’re in the regular season now. There are no excuses.”The Rangers want to be hard on the puck. They weren’t at least not nearly enough. They want to create sustained forecheck pressure and get to the front of the net. They didn’t do either again at least not nearly enough. They want to be — and have to be — crisp in their own end. They weren’t at least not much at all.

“You have to give credit where credit is due” Vigneault said the coach praising the Coyotes and goaltender Mike Smith’s puck-handling skills for negating the Blueshirts’ forecheck game. “Their goaltender handles the puck very well but we’re party responsible too because we have to put the puck in the corners which we weren’t that efficient at doing.”

The Rangers really weren’t very efficient at all. Though things were not as haphazard as they appeared throughout the exhibition season the Blueshirts still were way too sloppy. Shifts were too long. They didn’t marshal enough puck support on the rush and were out of the zone about as quickly as they could gain it throughout most of the up-tempo match.

They also were negligent at the other end especially below the hash marks and in front of the net where blunders allowed the Coyotes to seize control of the match that was tied 1-1 in the second until Radim Vrbata scored the second of his three goals at 7:08 soon after a Phoenix power play expired.